IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010                                                               ...
3318                                                                          IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO....
SALLES et al.: ELECTROMAGNETIC ANALYSIS OF SUBMARINE UMBILICAL CABLES                                                     ...
3320                                                                                     IEEE TRANSACTIONS ON MAGNETICS, V...
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Electromagnetic analysis of submarine umbilical cables with complex configurations


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Electromagnetic analysis of submarine umbilical cables with complex configurations

  1. 1. IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010 3317 Electromagnetic Analysis of Submarine Umbilical Cables With Complex Configurations M. B. C. Salles1 , M. C. Costa1 , M. L. P. Filho2 , J. R. Cardoso1 , and G. R. Marzo1 Applied Electromagnetism Laboratory (LMAG),PEA-EPUSP, São Paulo, Brazil Institute for Technological Research-IPT, São Paulo, Brazil These studies present the electromagnetic analyses of different configurations of the so called “Integrated Production Umbilical,” orsimply Umbilical Cables. Modern Umbilical Cables can have more than 4 independent 3-phase power circuits as well as steel tubes.There is no 2-D symmetry for these cable configurations and the 3-D simulations are very undesirable due to cable length. The adoptedmethodology to evaluate cable performance is a combination of 2-D-finite element analyses (coupled with electric circuit) and the trans-position technique. The results have shown that the configuration B in which all power circuits rotates along its own center has betterperformance considering the load terminal voltages due to the compensation of the induction effect along the cable. Index Terms—Finite element analysis, integrated production umbilical, power quality, submarine power cable, umbilical cable. I. INTRODUCTION pump. The main electrical characteristics of the voltage supplied by the converters (C1, C2, C3 and C4) are: frequency rangeT HE OIL exploration on offshore platforms represents an activity of high investment, where the risk of fails and themaintenance must be minimized. The oil exploration process ( – Hz); supply voltage ( constant; constant current ( A). – The cross-sections number 1 of the analyzed UC configura- V); V/Frequires cables composed by hydraulic steel tubes, independent tions are shown in Fig. 2 and in Fig. 3. One can see the 4 power3-phase power circuits, signal conductors, etc., these compo- circuits on the inner layer (configurations A and B) and on thenents can be integrated in an Umbilical Cable (UC). The new outer layer (configuration C) of the cables with their respectiveconcept of umbilical cables are composed by more than only phases A (dark grey), B (black) and C (white). Each power con-one independent power circuit operating in a wide range of vari- ductor has its own copper shield. There are 8 steel tubes in theable frequency and voltage values. The operation of the UC must outer layer (configurations A and B) and in the inner layer (con-follow strong power quality requirements. The UC internal con- figuration C) used to transport fluid. All configurations have anfiguration can affect the magnetic coupling between the compo- external metallic armor mainly used for mechanical purposes.nents derating the ampacity of the power circuits [1]–[3] and The outer diameter of the three configurations is 280 mm withalso degrading the quality of the voltage on the load terminals. 10 km of length. The main data of the cable are given in the There are no analytical equations to evaluate the interactions Appendix.inside the cables or to evaluate the power quality during oper- For better mechanical resistance, the internal structure of theation in unsymmetrical and complex geometries. Although the cable must rotate in relation to the center along its length. Inuse of 3-D-Finite Element Models overcomes the lack of ana- this specific case, the entire inner layer rotates in anticlockwiselytical equations, the number of finite elements required by this direction (1 turn every 1000 mm), while the entire outer layertype of cable geometry would lead to an undesirable simulation rotates in clockwise direction (1 turn every 1500 mm). In ad-time. In order to determine the voltage wave form at the load dition, the configuration B includes the rotation of each powerterminals, the authors has developed a combined methodology circuit in relation to its own center completing one turn everyto evaluate the mutual coupling effects between power conduc- 750 mm.The oil pump terminal voltages can be strongly affectedtors, power shields, metal tubes and armors (the metallic parts depending on the internal configuration of the UC. In order toinside the cable). This methodology combines the transmission guarantee the lifetime and the required maintenance of the oilline transposition method with 2-D-Finite Element Method re- pumps, the voltage at the load terminals should be not only bal-ducing drastically the simulation time with no loss of accuracy. anced but the influence of induced voltage from the surrounding This paper is organized as follows. In Section II, one presents conductors (modulation) should be minimized.the investigated geometries and the electrical characteristicsof the UC system. The combined methodology is presented in III. COMBINED METHODOLOGYSection III. Section IV discusses the results. In order to avoid the use of the 3-D models, one has developed a combined methodology using 2-D models and the transposi- II. DESCRIPTION OF UMBILICAL CABLE SYSTEMS tion technique. In the following, we briefly discuss the idea in- volved in this combined methodology to analyze complex Um- The analyzed configurations of the umbilical cable have four bilical Cables (UC).3-phase power circuits (Circuit #1, Circuit #2, Circuit #3 andCircuit #4). Each circuit feeds independently one submerged oil A. Limitations of the 2-D Finite Element (FE) Model As indicated in Section II, the analyzed cable has no sym- Manuscript received December 10, 2009; revised February 20, 2010; metry along the domain depth. The metallic components (con-accepted February 21, 2010. Current version published July 21, 2010. Corre- ductors, shields, tubes and armors) of UC change their relativesponding author: M. B. C. Salles (e-mail: Color versions of one or more of the figures in this paper are available online position along the cable length by performing a helicoidal Therefore, in order to analyze the cable performance the simu- Digital Object Identifier 10.1109/TMAG.2010.2044484 lations must consider different cross sections which represents 0018-9464/$26.00 © 2010 IEEE
  2. 2. 3318 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010Fig. 1. Unifilar diagram of the 3-phase system. Fig. 5. Cross sections used to represent the variation of relative position. C. Methodology: 2-D FE Model Transposition In this way, the cable performance is evaluated using 2-D finite element models coupled to the transposed multiple seg- ments technique (transposition) [4]. In the particular case of UC, the interchanges are obtained performing various 2-D steady- state analyses considering several cross sections to model the different relative positions between the power cables and the metallic components. D. Least Common Multiple (LCM)Fig. 2. Cross-sections number 1 of the configuration A and B. As described in Section II, the inner layer of this UC com- pletes 1 turn every 1000 mm while its outer layer completes 1 turn every 1500 mm. The LCM between the layer lengths is then 3000 mm. In other words, there is a repetition of the cable pat- tern every 3000 mm. E. Accuracy of the Analysis Method The number of cross sections defines the accuracy which is linked to the LCM of the cable layers, as shown in Fig. 5. For this UC one has compared the results for two values of cross sections number ( and ) and the difference was not significant. Fig. 7(a) presents 3 of the 50 cross sections used to compute the simulations of the configuration A and B.Fig. 3. Cross-sections number 1 of the configuration C. F. 2-D Finite Element Analysis From the electromagnetism theory, the induced voltage in one conductor increases proportionally with the level and the fre- quency of the current of the surrounded conductors. The con- verters supply the oil pumps with a constant relation between voltage and frequency. Considering the operation characteris- tics, one of the worst conditions is when 3 circuits #1, #2 and #3 supply the pumps on 80 Hz and 1 circuit #4 supplies on 30 Hz. The general idea of the methodology is summarized in Fig. 6.Fig. 4. Transmission Lines phase transposition. The computational package FLUX-2-D [6] is used to evaluate each cross section the configurations.the variation of the relative position between the metallic cable IV. UMBILICAL CABLE ANALYSIScomponents. In order to compare the performance of the UC with the eval-B. Transposition Technique uation of the coupling effects between the internal components, three different configurations are verified: The concept of transposition is addressed in classical 3-phase • Configuration A: the tubes and the power circuits turnhigh voltage transmission lines (TL) theory [4], [5]. The idea is around the cable center, but the power circuits do not turnto change the position of phases through the TL length, aiming around their own centers, as in Fig. 7(a).to obtain balanced values for the TL parameters (inductances, • Configuration B: the tubes and the power circuits turncapacitances and so on). The TL parameters are then calculated around the cable center and the power circuits turn alsofrom the average values on each phase. Fig. 4 illustrates a TL around their own centers, completing 1 turn every 750transposition with three interchanges with lengths L/3. mm, as shown in Fig. 7(b).
  3. 3. SALLES et al.: ELECTROMAGNETIC ANALYSIS OF SUBMARINE UMBILICAL CABLES 3319 Fig. 8. Magnetic potential lines obtained for the cross section 1 of the Config- uration A and B (only the first cross section has the same values). (a) 80 Hz, (b) 30 Hz.Fig. 6. General steps of the methodology. Fig. 9. Real components of induced voltage (80 Hz) in phase C of circuit #4—Configuration A.Fig. 7. Cross sections along the length of configurations A (a) and B (b). • Configuration C: the tubes and the power circuits turn around the cable center (Fig. 3). Due to the magnetic permeability of the armor ( u0),the boundary conditions were defined considering a tangentialmagnetic field in the outer diameter of the UC. The supply cir-cuits are modeled with ideal 3-phase voltage sources and the oilpumps are modeled as a pure resistive load of eight ohms oneach phase. The circuit coupling represents each finite elementregion (power conductors, power shields, tubes and armor) byan electric circuit component.A. Terminal Voltage Computation Fig. 10. Imaginary components of induced voltage (80 Hz) in phase C of circuit Fig. 8(a) shows the equipotential lines obtained from the anal- #4—Configuration A.ysis of the circuits #1, #2 and #3 supplied on 80 Hz. Fig. 8(b)shows the analysis of circuit #4 supplied on 30 Hz. These twoseparately analyses are necessary to determine the influence of Fig. 12. The induced voltage in configuration C (not showed)the 80 Hz on the 30 Hz circuits for frequency domain simulation. has similar performance of configuration A.The converter voltages of each phase A of the 3-phase circuitsare at its maximum value. B. Power Quality Analysis The average values of the real and the imaginary componentsof terminal voltage of the circuit #4 are calculated considering Voltage modulation indicates the induced voltage level in aeach cross section. The terminal voltage of the configuration A phase of a circuit by the surrounding circuits. The computationand B obtained by the combined methodology are shown from of the induced voltage on phase A of circuit as a result ofFigs. 9 to 12. current flowing through circuit can be calculated individually The induced voltages are almost constant for the configura- by the (1), (2) and (3)tion A, as shown in Fig. 9 and in Fig. 10. For the configurationB, the rotation of the 3-phase power circuits around their owncenters results on a variable induced voltage along the length (1)of the UC which compensates itself, as shown in Fig. 11 and in
  4. 4. 3320 IEEE TRANSACTIONS ON MAGNETICS, VOL. 46, NO. 8, AUGUST 2010 TABLE II SIMULATION DATA OF DIMENSIONS AND MATERIAL PROPERTIESFig. 11. Real components of induced voltage (80 Hz) in phase C of circuit Configuration B is the most appropriate one which guarantee#4—Configuration B. the balanced voltage at the load terminals and the low level of modulation on the most sensible circuit (30 Hz). V. CONCLUSION The combined methodology presented in this paper enables the evaluation of the power quality of UC using 2-D steady- state models, without compromising the accuracy of the results. One has verified that the rotation of the power circuits results in a reduction of the voltage modulation. These characteristics will also guarantee a better oil pump operation, diminishing the maintenance and enlarging the lifetime. This analysis gives faster results compared to 3-D steady- state or 2-D transient. Besides that, the results of the 2-D tran- sient analysis (not showed in this paper) for the configuration B are very similar to the one obtained by the frequency domain analysis. Even thought this methodology mainly analyses the in- duced voltage in the circuit #4 by the others 3 circuits, different analysis could also be done modifying the last two steps of theFig. 12. Imaginary components of induced voltage (80 Hz) in phase C of circuit Fig. 6, for example, to “loss computation” or “thermal analysis”.#4—Configuration B. APPENDIX TABLE I The main data of the cable geometry and the material prop- VOLTAGE MODULATION IN THE 30 HZ CIRCUIT (%) erties are given in Table II. ACKNOWLEDGMENT The authors gratefully acknowledge the financial support from the Brazilian government via FAPESP (State of São Paulo Research Foundation), CNPq (National Counsel of Technological and Scientific Development) and CAPES (“Co- ordenação de Aperfeiçoamento de Pessoal de Nível Superior,” in Portuguese). Computing total rms voltage on phase A of circuit , defining as load terminal voltage at fundamentalfrequency of circuit REFERENCES [1] P. Pettersson and N. Schönborg, “Reduction of power system magnetic field by configuration twist,” IEEE Trans. Power Del., vol. 12, no. 4, (2) pp. 1678–1683, Aug. 1997. [2] C. Demoulias, D. P. Labridis, P. S. Dokopoulos, and K. Gouramanis, Voltage modulation in phase A of circuit , is “Ampacity of low-voltage power cables under nonsinusoidal currents,” IEEE Trans. Power Del., vol. 22, no. 1, pp. 584–594, Feb. 2007. [3] F. de Leon and G. J. Anders, “Effects of backfilling on cable ampacity (3) analyzed with the finite element method,” IEEE Trans. Power Del., vol. 23, no. 2, pp. 537–543, Apr. 2008. [4] W. D. Stevenson, Elements of Power System Analysis. New York: The induced voltage on the oil pump terminal of circuit #4 McGraw-Hill, 1982. [5] C. R. Paul, Analysis of Multiconductor Transmission Lines. Newby the 80 Hz circuits were computed and compared with its York: Wiley-Interscience, 1994.terminal voltage feed on 30 Hz. Table I presents the modulation [6] FLUX-2-D—Finite Element Package for Electromagnetic Computa-values in the circuit #4. tions, [Online]. Available: